Re: Questions on impedance matching


Kevin Wood G7BCS
 

Thank you @KevinW.

Two questions to satisfy my academic mind...

(1) at what distance does it start to matter?
It would depend on your application but the cable length would need to be
significant in comparison with the wavelength of the signal when
propagating through the cable. At the maximum audio frequency likely to be
of interest - say 20 KHz, the wavelength, given a little reduction for the
velocity factor of the transmission line, is still going to be at least
10km, so line lengths of hundreds of metres would certainly suffer no real
issues from reflections due to mismatch.

(2) When you say the idea is for the input impedance to be so high that it
has no effect on the circuit, my understanding from the math is that as
you raise the load impedance, you're essentially tweaking the circuit
voltage too. For example, when source and load impedances match, the
circuit voltage is exactly half of the source voltage. But as you raise
the load impedance past that maximum power transfer point, the circuit
voltage continues to approach the maximum output voltage of the source.
So, is the idea of a 1 mega-ohm load virtually guarantee maximum voltage
since, in most cases, it will probably take up 99% of the total circuit
impedance?
Yes, that's the idea. The measured voltage tends towards the "open
circuit" voltage of your source. By loading the circuit with only a high
impedance, you can observe its operation with an oscilloscope without
modifying its behaviour by doing so. Incidentally, if 1M ohm is not
enough, you can switch to a "10x" probe and hit 10 M ohms at the cost of a
tenfold reduction in sensitivity.

As has also been pointed out, however, usually, when a generator specifies
its output impedance as 600 ohms (or 50 ohms, some are switchable) the
calibrated output voltage assumes it has been terminated with that
impedance. For this reason, your high impedance oscilloscope will probably
measure a level 6db higher unless you add a termination.

(3 -- extra credit): The input on my scope says 1 mega-ohm and 20 pF.
What's the reactance effect of the 20 pF and the net effect on load
impedance?
The 20pF indicates that there is a capacitive reactance component in
parallel with the scope's input impedance, so as you go higher in
frequency, the capacitive reactance tends to lower the input impedance. To
that you must also add the capacitance in any connecting cable and probe.
The reactance at 20pF hits about 400k ohms at 20 KHz, so it's starting to
become significant there...

When using 'scopes well into the megahertz it becomes the dominant
component of the input impedance.


Best Regards

Kevin

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